Tracing the Sources of Complexity in Evolution Peter Schuster - - PowerPoint PPT Presentation

Tracing the Sources of Complexity in Evolution Peter Schuster

Institut für Theoretische Chemie, Universität Wien, Austria and The Santa Fe Institute, Santa Fe, New Mexico, USA

Springer Complexity Lecture ICCS11 Wien, 12.09.2011

Web-Page for further information: http://www.tbi.univie.ac.at/~pks

1. Adaptation in biology 2. Cycles of evolution 3. Molecules – from sequence to function 4. Mutation and structure 5. Spaces and mappings 6. Evolutionary dynamics on landscapes 7. Neutrality 8. Stochasticity, contingency, and history 9. Perspectives

• 1. Adaptation in biology

2. Cycles of evolution 3. Molecules – from sequence to function 4. Mutation and structure 5. Spaces and mappings 6. Evolutionary dynamics on landscapes 7. Neutrality 8. Stochasticity, contingency, and history 9. Perspectives

system mechanism driving force external constraint result biomolecule evolutionary design better performance thermodynamic and kinetic stability functional biomolecules cell genetics and metabolism better usage of resources biochemical kinetics

• f metabolism

prokaryotic cell cell / molecule host/parasite coevolution mutual „arms races“ availability and survival of host cells viroids and viruses

• rganism

cell differentiation and development improvment by task splitting regulation and control

• f cell proliferation

multicellular

• rganism

population natural selection maximization of progeny resources limiting population size

• ptimized

variants ecosystem competition and coevolution adaptation to environments total carrying capacity speciation global climate changes singular events survival in new environments global sustainability new classes and phyla

Adaptation at different levels of complexity

system mechanism driving force external constraint result biomolecule evolutionary design better performance thermodynamic and kinetic stability functional biomolecules cell genetics and metabolism better usage of resources biochemical kinetics

• f metabolism

prokaryotic cell cell / molecule host/parasite coevolution mutual „arms races“ availability and survival of host cells viroids and viruses

• rganism

cell differentiation and development improvment by task splitting regulation and control

• f cell proliferation

multicellular

• rganism

population natural selection maximization of progeny resources limiting population size

• ptimized

variants ecosystem competition and coevolution adaptation to environments total carrying capacity speciation global climate changes singular events survival in new environments global sustainability new classes and phyla

Adaptation at different levels of complexity

system mechanism driving force external constraint result biomolecule evolutionary design better performance thermodynamic and kinetic stability functional biomolecules cell genetics and metabolism better usage of resources biochemical kinetics

• f metabolism

prokaryotic cell cell / molecule host/parasite coevolution mutual „arms races“ availability and survival of host cells viroids and viruses

• rganism

cell differentiation and development improvment by task splitting regulation and control

• f cell proliferation

multicellular

• rganism

population natural selection maximization of progeny resources limiting population size

• ptimized

variants ecosystem competition and coevolution adaptation to environments total carrying capacity speciation global climate changes singular events survival in new environments global sustainability new classes and phyla

Adaptation at different levels of complexity

system mechanism driving force external constraint result biomolecule evolutionary design better performance thermodynamic and kinetic stability functional biomolecules cell genetics and metabolism better usage of resources biochemical kinetics

• f metabolism

prokaryotic cell cell / molecule host/parasite coevolution mutual „arms races“ availability and survival of host cells viroids and viruses

• rganism

cell differentiation and development improvment by task splitting regulation and control

• f cell proliferation

multicellular

• rganism

population natural selection maximization of progeny resources limiting population size

• ptimized

variants ecosystem competition and coevolution adaptation to environments total carrying capacity speciation global climate changes singular events survival in new environments global sustainability new classes and phyla

Optimization at different levels of complexity

system mechanism driving force external constraint result biomolecule evolutionary design better performance thermodynamic and kinetic stability functional biomolecules cell genetics and metabolism better usage of resources biochemical kinetics

• f metabolism

prokaryotic cell cell / molecule host/parasite coevolution mutual „arms races“ availability and survival of host cells viroids and viruses

• rganism

cell differentiation and development improvment by task splitting regulation and control

• f cell proliferation

multicellular

• rganism

population natural selection maximization of progeny resources limiting population size

• ptimized

variants ecosystem competition and coevolution adaptation to environments total carrying capacity speciation global climate changes singular events survival in new environments global sustainability new classes and phyla

Adaptation at different levels of complexity

Three necessary conditions for Darwinian evolution are: 1. Multiplication, 2. Variation, and 3. Selection. None of the three conditions involves specific properties of the evolving entity except for the capability of reproduction:

Darwinian evolution is universal for reproducing objects no matter whether they are molecules or societies.

Charles Darwin, 1809-1882

Darwinian evolution, however, is not the only mechanism driving biological evolution.

system mechanism driving force external constraint result biomolecule evolutionary design better performance thermodynamic and kinetic stability functional biomolecules cell genetics and metabolism better usage of resources biochemical kinetics

• f metabolism

prokaryotic cell cell / molecule host/parasite coevolution mutual „arms races“ availability and survival of host cells viroids and viruses

• rganism

cell differentiation and development improvment by task splitting regulation and control

• f cell proliferation

multicellular

• rganism

population natural selection maximization of progeny resources limiting population size

• ptimized

variants ecosystem competition and coevolution adaptation to environments total carrying capacity speciation global climate changes singular events survival in new environments global sustainability new classes and phyla

Adaptation at different levels of complexity

system mechanism driving force external constraint result biomolecule evolutionary design better performance thermodynamic and kinetic stability functional biomolecules cell genetics and metabolism better usage of resources biochemical kinetics

• f metabolism

prokaryotic cell cell / molecule host/parasite coevolution mutual „arms races“ availability and survival of host cells viroids and viruses

• rganism

cell differentiation and development improvment by task splitting regulation and control

• f cell proliferation

multicellular

• rganism

population natural selection maximization of progeny resources limiting population size

• ptimized

variants ecosystem competition and coevolution adaptation to environments total carrying capacity speciation global climate changes singular events survival in new environments global sustainability new classes and phyla

Adaptation at different levels of complexity

system mechanism driving force external constraint result biomolecule evolutionary design better performance thermodynamic and kinetic stability functional biomolecules cell genetics and metabolism better usage of resources biochemical kinetics

• f metabolism

prokaryotic cell cell / molecule host/parasite coevolution mutual „arms races“ availability and survival of host cells viroids and viruses

• rganism

cell differentiation and development improvment by task splitting regulation and control

• f cell proliferation

multicellular

• rganism

population natural selection maximization of progeny resources limiting population size

• ptimized

variants ecosystem competition and coevolution adaptation to environments total carrying capacity speciation global climate changes singular events survival in new environments global sustainability new classes and phyla

Adaptation at different levels of complexity

1. Adaptation in biology

• 2. Cycles of evolution

3. Molecules – from sequence to function 4. Mutation and structure 5. Spaces and mappings 6. Evolutionary dynamics on landscapes 7. Neutrality 8. Stochasticity, contingency, and history 9. Perspectives

Genotypes, phenotypes, and fitness

Genotypes, phenotypes, and fitness

1. Adaptation in biology 2. Cycles of evolution

• 3. Molecules – from sequence to function

4. Mutation and structure 5. Spaces and mappings 6. Evolutionary dynamics on landscapes 7. Neutrality 8. Stochasticity, contingency, and history 9. Perspectives

Make things as simple as possible, but not simpler !

Albert Einstein

Albert Einstein‘s razor, precise refence is unknown.

The paradigm of structural biology

The paradigm of structural biology

The paradigm of structural biology

The paradigm of structural biology

The paradigm of structural biology

The three-dimensional structure of a short double helical stack of B-DNA 1953 – 2003 fifty years double helix

James D. Watson, 1928-, and Francis H.C. Crick, 1916-2004 Nobel prize 1962

A symbolic notation of RNA secondary structure that is equivalent to the conventional graphs Criterion: Minimum free energy (mfe) Rules: _ ( _ ) _  {AU,CG,GC,GU,UA,UG} N = 4n NS < 3n

The logics of DNA replication Taq = thermus aquaticus

1. Adaptation in biology 2. Cycles of evolution 3. Molecules – from sequence to function

• 4. Mutation and structure

5. Spaces and mappings 6. Evolutionary dynamics on landscapes 7. Neutrality 8. Stochasticity, contingency, and history 9. Perspectives

Nucleobase and base pair mutations

Nucleobase and base pair mutations

Nucleobase and base pair mutations

A case study: A simple RNA molecule

1. Adaptation in biology 2. Cycles of evolution 3. Molecules – from sequence to function 4. Mutation and structure

• 5. Spaces and mappings

6. Evolutionary dynamics on landscapes 7. Neutrality 8. Stochasticity, contingency, and history 9. Perspectives

The inverse folding algorithm searches for sequences that form a given RNA secondary structure under the minimum free energy criterion.

Inversion of genotype-phenotype mapping

Neutral networks in sequence space

Realistic fitness landscapes 1.Ruggedness: nearby lying genotypes may unfold into very different phenotypes 2.Neutrality: many different genotypes give rise to phenotypes with identical selection behavior

1. Adaptation in biology 2. Cycles of evolution 3. Molecules – from sequence to function 4. Mutation and structure 5. Spaces and mappings

• 6. Evolutionary dynamics on landscapes

7. Neutrality 8. Stochasticity, contingency, and history 9. Perspectives

Three necessary conditions for Darwinian evolution are: 1. Multiplication, 2. Variation, and 3. Selection. All three conditions are fulfilled not only by cellular organisms but also by nucleic acid molecules – DNA or RNA – in suitable cell-free experimental assays:

Darwinian evolution in the test tube

Charles Darwin, 1809-1882

Evolution in the test tube: G.F. Joyce, Angew.Chem.Int.Ed. 46 (2007), 6420-6436

Kinetics of RNA replication

C.K. Biebricher, M. Eigen, W.C. Gardiner, Jr. Biochemistry 22:2544-2559, 1983

Christof K. Biebricher, 1941-2009

RNA replication by Q-replicase

• C. Weissmann, The making of a phage.

FEBS Letters 40 (1974), S10-S18

C.K. Biebricher, R. Luce. 1992. In vitro recombination and terminal recombination of RNA by Q replicase. The EMBO Journal 11:5129-5135. stable

does not replicate!

metastable

replicates!

Manfred Eigen 1927 -

  

  

   

n i i n i i i j i n i ji j

x x f Φ n j Φ x x W x

1 1 1

, , 2 , 1 ; dt d 

Mutation and (correct) replication as parallel chemical reactions

• M. Eigen. 1971. Naturwissenschaften 58:465,
• M. Eigen & P. Schuster.1977. Naturwissenschaften 64:541, 65:7 und 65:341

Mutation-selection equation: [Ii] = xi  0, fi > 0, Qij  0 Solutions are obtained after integrating factor transformation by means

• f an eigenvalue problem

f x f x n i x x Q f dt dx

n j j j n i i i j n j ji j i

     

  

   1 1 1

; 1 ; , , 2 , 1 ,   

         

) ( ) ( ; , , 2 , 1 ; exp exp

1 1 1 1

   

     

      

n i i ki k n j k k n k jk k k n k ik i

x h c n i t c t c t x     

     

n j i h H L n j i L n j i Q f W

ij ij ij i

, , 2 , 1 , ; ; , , 2 , 1 , ; ; , , 2 , 1 , ;

1

          



 

1 , , 1 , ;

1

      



n k L W L

k

 

quasispecies

The error threshold in replication and mutation

driving virus populations through threshold

Model fitness landscapes I

single peak landscape step linear landscape

Error threshold on the single peak landscape

Error threshold on the step linear landscape

Model fitness landscapes II linear and multiplicative hyperbolic

The linear fitness landscape shows no error threshold

Rugged fitness landscapes

• ver individual binary sequences

with n = 10

single peak landscape „realistic“ landscape

Error threshold: Individual sequences n = 10,  = 2, s = 491 and d = 0, 0.5, 0.9375

Case I: Strong quasispecies n = 10, f0 = 1.1, fn = 1.0, s = 919

d = 0.5 d = 1.0

Case III: multiple transitions n = 10, f0 = 1.1, fn = 1.0, s = 637

d = 0.995 d = 1.0

1. Adaptation in biology 2. Cycles of evolution 3. Molecules – from sequence to function 4. Mutation and structure 5. Spaces and mappings 6. Evolutionary dynamics on landscapes

• 7. Neutrality

8. Stochasticity, contingency, and history 9. Perspectives

Motoo Kimuras population genetics of neutral evolution. Evolutionary rate at the molecular level. Nature 217: 624-626, 1955. The Neutral Theory of Molecular Evolution. Cambridge University Press. Cambridge, UK, 1983.

Motoo Kimura

Is the Kimura scenario correct for frequent mutations?

Pairs of neutral sequences in replication networks

• P. Schuster, J. Swetina. 1988. Bull. Math. Biol. 50:635-650

5 . ) ( ) ( lim

2 1

 



p x p x

p

dH = 1

a p x a p x

p p

  

 

1 ) ( lim ) ( lim

2 1

dH = 2

Random fixation in the sense of Motoo Kimura

dH  3

1 ) ( lim , ) ( lim

• r

) ( lim , 1 ) ( lim

2 1 2 1

   

   

p x p x p x p x

p p p p

A fitness landscape including neutrality

Neutral network: Individual sequences n = 10,  = 1.1, d = 0.5

Neutral network: Individual sequences n = 10,  = 1.1, d = 0.5

Consensus sequence of a quasispecies with strongly coupled sequences of Hamming distance

dH(Xi,,Xj) = 1 and 2.

Complexity in molecular evolution

W = G  F 0 , 0  largest eigenvalue and eigenvector

diagonalization of matrix W „ complicated but not complex “ fitness landscape mutation matrix „ complex “ ( complex )

sequence  structure

„ complex “

mutation selection

1. Adaptation in biology 2. Cycles of evolution 3. Molecules – from sequence to function 4. Mutation and structure 5. Spaces and mappings 6. Evolutionary dynamics on landscapes 7. Neutrality

• 8. Stochasticity, contingency, and history

9. Perspectives

Evolution in silico

• W. Fontana, P. Schuster,

Science 280 (1998), 1451-1455

The flowreactor as a device for studies of evolution in vitro and in silico Replication rate constant: fk =  / [ + dS

(k)]

dS

(k) = dH(Sk,S)

Selection constraint: Population size, N = # RNA molecules, is controlled by the flow Mutation rate: p = 0.001 / site  replication N N t N   ) (

In silico optimization in the flow reactor: Evolutionary Trajectory

RNAphe as target structure Randomly chosen initial structure

RNAphe as target structure Randomly chosen initial structure

RNAphe as target structure Randomly chosen initial structure

RNAphe as target structure Randomly chosen initial structure

Spreading of the population

• n neutral networks

Drift of the population center in sequence space Evolutionary trajectory

Bacterial evolution under controlled conditions: A twenty years experiment. Richard Lenski, University of Michigan, East Lansing

Richard Lenski, 1956 -

Epochal evolution of bacteria in serial transfer experiments under constant conditions

• S. F. Elena, V. S. Cooper, R. E. Lenski. Punctuated evolution caused by selection of rare beneficial mutants.

Science 272 (1996), 1802-1804 1 year

Epochal evolution of bacteria in serial transfer experiments under constant conditions

• S. F. Elena, V. S. Cooper, R. E. Lenski. Punctuated evolution caused by selection of rare beneficial mutants.

Science 272 (1996), 1802-1804 1 year

The twelve populations of Richard Lenski‘s long time evolution experiment Enhanced turbidity in population A-3

Innovation by mutation in long time evolution of Escherichia coli in constant environment Z.D. Blount, C.Z. Borland, R.E. Lenski. 2008. Proc.Natl.Acad.Sci.USA 105:7899-7906

Contingency of E. coli evolution experiments

1. Adaptation in biology 2. Cycles of evolution 3. Molecules – from sequence to function 4. Mutation and structure 5. Spaces and mappings 6. Evolutionary dynamics on landscapes 7. Neutrality 8. Stochasticity, contingency, and history

• 9. Perspectives

(i) Fitness landscapes for the evolution of molecules are obtainable by standard techniques of physics and chemistry. (ii) Fitness landscapes for evolution of viroids and viruses under controlled conditions are accessible in principle. (iii) Systems biology can be carried out for especially small bacteria and an extension to bacteria of normal size is to be expected for the near future. (iv) The computational approach for selection on known fitness landscapes – ODEs or stochastic processes – is standard. (v) The efficient description of migration and splitting

• f populations in sequence space requires new

mathematical techniques.

Consideration of multistep and nonlinear replication mechanisms as well as accounting for epigenetic phenomena is readily possible within the molecular approach.

Coworkers

Walter Fontana, Harvard Medical School, MA Matin Nowak, Harvard University, MA Ivo L.Hofacker, Christoph Flamm, Andreas Svrček-Seiler, Universität Wien, AT Peter Stadler, Bärbel Stadler, Universität Leipzig, GE Sebastian Bonhoeffer, ETH Zürich, CH Christian Reidys, University of Southern Denmark, Odense, DK Christian Forst, University of Texas Southwestern Medical Center, TX Kurt Grünberger, Michael Kospach, Andreas Wernitznig, Stefanie Widder, Stefan Wuchty, Universität Wien, AT Jan Cupal, Ulrike Langhammer, Ulrike Mückstein, Jörg Swetina, Universität Wien, AT Ulrike Göbel, Walter Grüner, Stefan Kopp, Jaqueline Weber, Institut für Molekulare Biotechnologie, Jena, GE

Universität Wien

Universität Wien

Acknowledgement of support

Fonds zur Förderung der wissenschaftlichen Forschung (FWF) Projects No. 09942, 10578, 11065, 13093 13887, and 14898 Wiener Wissenschafts-, Forschungs- und Technologiefonds (WWTF) Project No. Mat05 Jubiläumsfonds der Österreichischen Nationalbank Project No. Nat-7813 European Commission: Contracts No. 98-0189, 12835 (NEST) Austrian Genome Research Program – GEN-AU Siemens AG, Austria Universität Wien and the Santa Fe Institute

Thank you for your attention !

Web-Page for further information: http://www.tbi.univie.ac.at/~pks